Collisionless Boltzmann equation approach for the study of stellar discs within barred galaxies

We study the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar. We carry out the analysis by developing a numerical resolution of the 2D2V Collisionless Boltzmann Equation (CBE) and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood. We recover similar results to these obtained by different authors using N-body simulations, but we can also numerically identify faint structures thanks to the canceling of the Poisson noise. We find that the ratio of the bar pattern speed to the local circular frequency is in the range $\Omega_B/\Omega$ = 1.77 to 1.91. If the Galactic bar angle orientation is within the range from 24 to 45 degrees, the bar pattern speed is between 46 and 49 km/s/kpc.